六维时空中具有非平凡拓扑的视视界与超环猜想
Apparent Horizons with Nontrivial Topology and the Hyperhoop Conjecture in Six-Dimensional Space-Times
摘要：
我们研究了hyperhoop猜想的有效性，hyperhoop猜想确定了在高维时空中形成黑洞视界的一个充分必要条件。在这里，我们考虑瞬时静态，共形平坦的初始数据集，每个描述一个引力场的均匀质量k球源，k= 1，2，在五维柯西表面。数值结果表明超箍猜想在较宽的模型参数范围内是有效的。我们还首次证实了S**2 x S**2或S**1 x S**3的视视界同胚的存在性，这是黑环的高维推广。
英文摘要：
We investigate the validity of the hyperhoop conjecture, which claims to determine a necessary and sufficient condition for the formation of black hole horizons in higher-dimensional space-times. Here we consider momentarily static, conformally flat initial data sets each describing a gravitational field of uniform massive k-sphere sources, for k=1,2, on the five-dimensional Cauchy surface. The numerical result shows the validity of the hyperhoop conjecture for a wide range of model parameters. We also confirm for the first time the existence of an apparent horizon homeomorphism to S**2 x S**2 or S**1 x S**3, which is a higher-dimensional generalization of the black ring.
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